Waco, Tex.

When Edward B. Burger presents a math challenge to his class at Baylor University, he paces the aisles and pairs students together. "I want to hear chattering," he says. Before long, students are laughing and shouting out answers. He dashes to the chalkboard to scribble them down, creating long rows of numbers topped with running stick figures.

Mr. Burger, 46, who is visiting from Williams College, keeps up a rapid-fire banter with his students, whom he calls by name.

He is here this semester as a recipient of Baylor's annual Robert Foster Cherry Award for Great Teaching, which came with $215,000 in cash and $35,000 for Williams's math department.

The 12-member committee that culled more than 100 nominations from around the country was impressed with his string of teaching awards, his multimedia textbooks and videos for secondary schools, and his televised analysis of the math behind the 2010 Winter Olympics.

Mr. Burger was younger than the students he's teaching at Baylor when he discovered how much fun teaching math could be. Armed with a lesson plan and a conviction that he could cut through his classmates' collective fog, he asked his high-school teacher if she'd step aside and let him teach two classes.

"She agreed, and at the age of 17, I stood up in front of a precalculus class of about 40 students who looked at me like I was the biggest nerd in the world," says Mr. Burger.

He began teaching night classes at Austin Community College at age 22, while he was working on his doctorate at the University of Texas at Austin. "What I was trying to do was to take really complex, intricate, abstract ideas of mathematics and make them come to life for these students," he says. He began encouraging students to be creative and take risks, and even bases a portion of their grades on "the quality of their failure."

He judges that quality, he says, "by the size of the risk they've taken and the amount of insight they have generated from their mistakes."

In 1990 he received a tenure-track position at Williams, where he is also a professor of social responsibility and personal ethics. The most important issue, he says, is what students will retain from his class 10 years later. "If we are in the business of transforming lives and can't give a good answer to that question," he says, "we're failing."

To demonstrate the concept of infinity to a class of mostly liberal-arts students at Baylor, he sketches a trough that he describes as containing an infinite number of Ping-Pong balls, which are falling into a barrel, 10 at a time, as a hypothetical student reaches in and plucks balls out at shorter and shorter intervals.

"Soon you'll be working faster than the speed of sound, than the speed of light. You black out, regain consciousness, approach the barrel, look inside. My question to you is, 'What's inside? What is in the barrel?'"

The students pair up at their desks and compare guesses. "It has to be infinity," one says. His partner responds, "He's trying to trick us. ... Maybe the answer's zero." Mr. Burger writes these and other guesses, which he draws out of more-hesitant students, on the board. He tells the class to come back on Tuesday for the answer.

Adam Telatovich, a sophomore math major, says some of his favorite lessons in Mr. Burger's number-theory class follow that pattern. "He starts out with a big picture, describing these really far-out problems, and says this is what we're going to work up to. Then he builds up suspense and leaves the punch line for the next class. When the class is over, we're disappointed."

Lance L. Littlejohn, chairman of the department of mathematics at Baylor, describes Mr. Burger as "a teaching phenomenon": well organized, articulate, and engaging.

At Williams, when his students arrive for the first day of class, they sometimes tell him that they've already had him in a course. That's because he wrote an online, multimedia math textbook used in many classrooms nationwide. California just started a pilot program in which middle-school students are given iPads to read his textbook and watch his lecture series.

Mr. Burger, who once planned to go to law school, discourages students from zeroing in too early on a career. "The whole point of higher education is to mess things up and challenge basic assumptions about how you look at the world and fit into it," he says. "If you don't allow your education to challenge those assumptions, there's no point in it."

He advises students to choose their careers by finding things they would do on their own for fun. "On good days," he says, "I almost feel it's criminal to accept money for what I do."

This fall he's stimulating discussion about good teaching across the Baylor campus by helping to organize weekly lunch discussions for faculty members. He will also speak this week to a regional meeting of K-12 math teachers and plans to visit local public schools to meet with math teachers and students. "He's wonderful in the college classroom," says Heidi J. Hornik, a professor of art history and chair of the Cherry award committee, "but he also reaches deep down into the academic system to make math exciting for everyone."

By the way, the answer to the question about the number of Ping-Pong balls in the barrel: zero.

## Comments

1. plclark - October 07, 2010 at 02:33 am

Your chronology of Professor Burger's early career looks inaccurate. The way the sentence "He earned a doctorate..." is written suggests that Prof. Burger was 22 at the time. The wikipedia article on him says that he was born in 1964 and received his PhD in 1990, so in fact he was either 25 or 26. Similarly, he started his tenure track job at Williams until 1990, so I don't see how he could have been 24 at the time.

2. plclark - October 07, 2010 at 02:35 am

"started his tenure track job at Williams IN 1990", I should have said.

3. kmangan - October 07, 2010 at 08:55 pm

I've clarified the chronology to show that Prof. Burger was teaching at ACC while completing his doctorate. Thanks for your comments.

4. impossible_exchange - October 08, 2010 at 08:52 am

A teaching phenomenon, a math person who actually teaches rather than reinforces a false notion of merit as the reason why some get it and others don't.

Too often math and science are taught as chores, a sort of initiation rite, and either you pass through it or you fail to.

All fundamentally smart things are interesting and easy to learn.

Math is a smart thing.

Thus...

5. philosophy - October 08, 2010 at 10:54 am

I need an explanation about the barrel . . .

6. dank48 - October 08, 2010 at 11:31 am

The idea is that the barrel or trough or whatever contains an infinite number of balls. An infinite number are removed. So infinity minus infinity equals zero.

This is one of the more vivid ways of helping students realize that things aren't always cut and dried in mathematics. I can just imagine how Mr. Burger gets across to them that the number of integers equals the number of even integers. . . .

7. mrrosever - October 08, 2010 at 03:47 pm

Imagine an infinite number of boys in red jerseys on rollerskates with numbers 1, 2, 3, 4 .... on front and back on sports team jerseys.

Imagine also an infinite number of girls in blue jerseys with even numbers 2, 4, 6, 8 .... displayed on the front and back in a similar manner.

Both groups are skating around in space when the sign for "couples skate" comes on. Now there is confusion. Everyone is looking for a partner but the guys are boys seem anxious. They seem to think if they don't hurry they will miss out on teh skate becuase their are less girls. Oh no! To clear the air though, the DJ announces "If your a boy find the girl with double your number, if your a girl cut your number in half. That is your partner." Though it takes some time for evryone to pair up, the worry is alleviated. Somewhere there is a partner for every boy and girl.

Though both groups are infinite in size and one strangely is a propersubset of the other, there are equally many integers demonstrated as evens. Demonstrated in the fact that everyone has a skate partner.

That's how I explain it.

8. mrrosever - October 08, 2010 at 03:48 pm

not the best typist and running to a meeting but I hope you like the idea.

9. philosophy - October 08, 2010 at 04:10 pm

I get the infinity minus infinity, and the # of even integers is the same as the # (if it's ok to call infinity a "number") of all integers. What I don't get is the claim that an infinity of balls were removed from the barrel. Seems to me that when the student blacks out, the balls would continue to fall into the barrel, so there would be lots of them in the barrel when the student wakes up, no matter how fast they were previously removed. Faster than the speed of light isn't infinitely fast.

10. 11193335 - October 08, 2010 at 04:17 pm

I like the idea.

11. commserver - October 08, 2010 at 05:53 pm

My daughter is a sophomore at Williams. She had him last year for multivariate calculus and was impressed

12. mystery345 - October 09, 2010 at 05:42 pm

We are big fans of Professor Burger at my house. When my son was 11, he discovered him online while working through one of his math textbook during the summer. He was able to successfully complete the entire textbook simply by watching the online tutorials, AND he enjoyed it. Fast forward to last week. While trying to explain an algebra problem to my son one evening he looked at me like I was from Mars and said, maybe I should have Professor Burger explain it. He then walked off and opened his laptop and I was no longer tutoring him.

We live in one of the school districts with the iPad pilot program (unfortunately, not at my son's middle school) and when my son saw professor Burger on TV he yelled to me to come quick, "It's professor Burger on the news!" I am glad to see an article in the CHE that praises his work. He has really inspired my son who wants to major in math when he goes to college.

13. orage - October 10, 2010 at 12:08 pm

I'm not sure the ping pong ball problem is fully stated. For there to be zero at the end, I think you have to have numbered the balls and be removing them in order, starting at 1. If you don't number the balls, then the answer is much more fun. There could be any number, from 0 to infinty, left in the barrel.

14. ellenhunt - October 11, 2010 at 01:20 pm

What 9 said. And if you are going to black out, that physiology would happen long before moving your hands at the speed of sound. :-)

But I like this. Good on him.

15. partial_order - October 27, 2010 at 07:00 pm

The example of the trough with an infinite number of balls in it doesn't make sense to me. There's surely something missing in the description of this problem. Is there a link somewhere to this problem? I think everyone who has read this article would appreciate that.